Yes, it should be legal for homosexual people to adopt children. People who are gay or lesbian are able to parent on a similar level as heterosexual couples. A child adopted into a gay or lesbian family still has two parents who are capable of providing care and attention. With the amount of children who are active in the adoption and foster system, it only makes sense to allow more couples to adopt.
Few people would argue with the idea that there should be regulations as to who should be able to legally adopt children. However, sexuality should not be one of those regulations. There is no evidence that heterosexual people make better parents, or are more likely to have healthy households, than homosexual people. The only reason to ban homosexual people from adopting is the idea that homosexuality is somehow morally wrong, and that conceit is a personal opinion which should not influence legislation.
Many children are stuck in orphanages or homeless, without the care and shelter of parents. Homosexual people that are willing to adopt these children should be able to do so, provided that they can provide them with the care and support they need to grow up and become productive members of society.
Many studies and personal experiences have shown that children need both the influence of a mother and a father to develop appropriately in their relationships and social skills. Because of this, I don't believe single people should be allowed to adopt either, regardless of their sexual orientation. Children learn and grow in different ways when they interact with a mother and a father.